1. Climate Modeling In -Class Discussion: Energy Balance Models

2. 1.Net radiation in/out at any latitude balanced by dynamical divergence/convergence 2.Still require global radiative balance Solve this equation to get T s (  ). Energy Balance Equation Suppose Earth has interior source of heat, like Jupiter. How does the balance equation change?

3. Energy Balance Equation

4. Boundary Conditions: (i)Dynamic flux = 0 at poles (x = 1) (ii) Dynamic flux = 0 at x = 0 (hemispheric symmetry) (iii) x i = x(T s = -10˚C) => x i = x(I i =195.7 W-m -2 ) Balance Equation to Solve Where

5. What happens to the solution? Suppose the interior heating gradually disappears. How do the balance equation and the equilibrium solution change? Balance Equation to Solve Where

6. Solar Flux - 2 S(x) is an even function about 0. Suppose Earth's tilt of axis changes. How does this picture change?

7. Solar Flux - 2 S(x) is an even function about 0. Suppose Earth's tilt of axis changes. How does this picture change, if … 

8. Solar Flux - 2 S(x) is an even function about 0. … the earth has zero tilt? (no seasons) 

9. Solar Flux - 2 S(x) is an even function about 0.  … the earth has 90˚ tilt? (like Uranus)

10. For any variable use, e.g., Annual Cycle - Representation  Units for t: year  P 1 captures seasonal asymmetry about equator (e.g. SH warm when NH cold.)  Sizes of T 1C and T 1S determine amplitude and phase of annual cycle  Fit observed T, I, albedo and S: rms error < 5%

11. For any variable use, e.g., Annual Cycle - Representation  P 1 captures seasonal asymmetry about equator (e.g. SH warm when NH cold.)  Sizes of T 1C and T 1S determine amplitude and phase of annual cycle  How do these change for the cases of no axial tilt or 90˚ tilt?

12. Albedo - 2 x i = ice/snow edge = 0.95 (lat i = 72˚)

13. Albedo - 2 How would this change if clouds were different?

14. In-Class Discussion ~ End ~